McArdle glanced home a corner from substitute Raffaele De Vita at the neat post to reward more than 1,000 travelling fans amid an impressive opening-day League One gate of 13,862.
The Robins went in front after just 13 minutes when Scott Wagstaff fired home right-footed from 12 yards after Jay Emmanuel-Thomas had forced his way into the penalty area.
The hosts looked comfortable until a defensive mix-up after 33 minutes saw James Hanson break between City's defence.
Goalkeeper Frank Fielding elected to race out to the corner of his penalty area and Hanson rounded him before crossing for Nahki Wells to shoot past the only covering defender on the line.
Emmanuel-Thomas slotted home left-footed from a Sam Baldock cross after 58 minutes to restore Bristol's advantage, but McArdle had the final say as the game entered the closing stages.